Optical fiber grating device

ABSTRACT

An optical fiber grating device  1  is a device in which a long period grating  14  is formed in a core region  11  of an optical fiber  10  consisting of the core region  11  having a refractive index n 1  and an outside diameter  2   a , a first cladding region  12  surrounding the core region  11  and having a refractive index n 2  and an outside diameter  2   b , and a second cladding region  13  surrounding the first cladding region  12  and having a refractive index n 3  and an outside diameter  2   c . There is a magnitude relation of n 1 &gt;n 2 &gt;n 3  among the refractive index n 1  of the core region  11 , the refractive index n 2  of the first cladding region  12 , and the refractive index n 3  of the second cladding region  13 , a relative refractive index difference Δn 2  of the first cladding region  12  to the second cladding region  13  is not less than 0.5%, and a thickness (c−b) of the second cladding region  13  with respect to a transmission loss peak wavelength λ is in a range of not less than λ nor more than 10λ.

TECHNICAL FIELD

[0001] The present invention relates to an optical component suitablyapplicable in optical communication and others and, more particularly,to an optical fiber grating device in which a long period grating isformed in the core region of optical fiber. The long period gratingherein, for example as disclosed in U.S. Pat. No. 5,703,978, convertslight of a selected wavelength out of the core mode propagating asconfined in the core region, into cladding mode and radiates thecladding mode into the outside of the cladding region, different fromshort period gratings which reflect light of a selected wavelength.

BACKGROUND ART

[0002] The optical fiber grating devices with the long period grating inthe core region of optical fiber are able to bring about couplingbetween the core mode of a predetermined wavelength and the claddingmode through periodic perturbations of the grating. Namely, the opticalfiber grating devices transfer power of the core mode of thepredetermined wavelength to the cladding mode on a wavelength selectivebasis. Here the core mode is a mode propagating as confined in the coreregion of optical fiber. On the other hand, the cladding mode is a moderadiated into the cladding region around the core region, without beingconfined in the core region of optical fiber. Such optical fiber gratingdevices have been used as optical fiber filters in the fields of opticalcommunications, selectively cutting off core mode of a predeterminedwavelength (transmission loss peak wavelength) from among those of acertain wavelength band having propagated in optical fiber.

[0003] The cladding mode is a mode taking account of the entire fiberregion defined at the interface between the cladding region and an outerlayer such as an air layer or a coating layer. Accordingly, a change inthe refractive index of the outer layer results in shifting thewavelength of coupling between core mode and cladding mode, i.e., thetransmission loss peak wavelength and also changing the transmissionloss of the core mode at the transmission loss peak wavelength.Particularly, where the optical fiber is coated with a resin having arefractive index close to that of glass, no cladding mode is formed, soas to result in no transmission loss peak wavelength in the opticalfiber grating device. For this reason, the optical fiber grating devicehad the problem that the coating intended for protection thereof was notapplicable.

[0004] The optical fiber grating device disclosed in Japanese PatentApplication Laid-Open No. 11-326654 is one proposed in order to solvethis problem, in which the long period grating is formed in asilica-based single-mode fiber having a refractive index profile of dualshape core (DSC) structure. Here the refractive index profile of DSCstructure is of a structure including a first core region with arefractive index n₁, a second core region with a refractive index n₂,and a cladding region with a refractive index n₃ in the order named fromthe center of the optical axis (where n₁>n₂>n₃). This optical fibergrating device is a device wherein GeO₂ is added to both the first coreregion and the second core region of the optical fiber and they areexposed to spatially intensity-modulated ultraviolet light to form indexmodulation or a grating across these two regions. In this optical fibergrating device, the core mode of a predetermined wavelength propagatingin the first core region is coupled with a higher order mode propagatingin both the first core region and the second core region to cut off thecore mode of the predetermined wavelength.

[0005] The aforementioned Application describes that the preferredrefractive index profile in the optical fiber grating device asdisclosed in the Application is such that the relative refractive indexdifference of the first core region is in the range of 0.8% to 1.0%, therelative refractive index difference of the second core region in therange of 0.05% to 0.15%, the radius of the first core region in therange of 3.2 μm to 3.8 μm, and the radius of the second core region inthe range of 17 μm to 20 μm.

DISCLOSURE OF THE INVENTION

[0006] The inventors investigated the above-stated prior art and foundthe following problem.

[0007] Namely, since this optical fiber grating device includes fewhigher modes propagating in both the first core region and the secondcore region, the number of transmission loss peaks is approximately 1 or2 in the operating wavelength band. Accordingly, freedom of setting thegrating period becomes small, when the grating period is set information of the grating so as to yield a desired transmission loss peakwavelength in the optical fiber grating device. Since the couplingcoefficient is large between the core mode of the predeterminedwavelength propagating in the first core region and the higher ordermode propagating in both the first core region and the second coreregion, change is large in the transmission loss and the transmissionloss peak wavelength against increase of refractive index due to theexposure to the ultraviolet light and it is thus difficult to achievecontrol to satisfy both the predetermined transmission loss and thetransmission loss peak wavelength.

[0008] The present invention has been accomplished in order to solve theabove problem and an object of the invention is to provide an opticalfiber grating device giving high degrees of freedom in the setting ofthe grating period and permitting easy control of the transmission lossand the transmission loss peak wavelength.

[0009] An optical fiber grating device according to the presentinvention is an optical fiber grating device in which a long periodgrating is formed in a core region of an optical fiber comprising a coreregion having a refractive index n₁ and an outside diameter 2 a, a firstcladding region surrounding the core region and having a refractiveindex n₂ and an outside diameter 2 b, and a second cladding regionsurrounding the first cladding region and having a refractive index n₃and an outside diameter 2 c. There is a magnitude relation of n₁>n₂>n₃among the refractive index n₁ of the core region, the refractive indexn₂ of the first cladding region, and the refractive index n₃ of thesecond cladding region. A relative refractive index difference of thefirst cladding region to the second cladding region is not less than0.5%. A thickness (c−b) of the second cladding region with respect to atransmission loss peak wavelength λ is in a range of not less than λ normore than 10λ.

[0010] This optical fiber grating device includes many transmission losspeaks in a predetermined wavelength band (e.g., 1.2 μm to 1.8 μm) andthe spacing is small between the transmission loss peaks. The couplingcoefficient is small between the core mode and the higher order modepropagating in the first cladding region, so that variation is reducedin the transmission loss and the transmission loss peak wavelengthagainst refractive index change. Further, there is little influence fromthe outer layer outside the second cladding region, the transmissionloss characteristics are stable, and the excellent cutoff effect isachieved in the grating. Accordingly, freedom of setting the gratingperiod becomes large, controlling of the transmission loss and thetransmission loss peak wavelength gets easy, and excellent transmissionloss characteristics is obtained in this optical fiber grating device.

[0011] In the optical fiber grating device according to the presentinvention, the relative refractive index difference of the firstcladding region to the second cladding region is preferably not lessthan 0.5% nor more than 1.5%. When the second cladding region is dopedwith the fluorine (F) element, the refractive index n₃ of the secondcladding region can be made lower than the refractive index n₂ of thefirst cladding region and the relative refractive index difference ofthe first cladding region to the second cladding region can be increasedup to 1.5%.

[0012] In the optical fiber grating device according to the presentinvention, a resin coating having a refractive index n₄ (where n₄>n₂) ispreferably provided around the second cladding region. Thisconfiguration favorably facilitates guiding of higher order modegenerated by mode coupling at the transmission loss peak wavelength tothe outside of the optical fiber. This structure is also preferable interms of protection of the optical fiber grating device.

[0013] In the optical fiber grating device according to the presentinvention, the outside diameter 2 b of the first cladding region ispreferably not less than 100 μm. This configuration is preferable inthat the number of transmission loss peaks is large and also preferablein that the excellent cutoff effect is obtained.

[0014] In the optical fiber grating device according to the presentinvention, a mode field diameter of fundamental mode propagating in thecore region is preferably not more than one tenth of the outsidediameter 2 b of the first cladding region. This configuration ispreferable in that the number of transmission loss peaks is large andalso preferable in that the excellent cutoff effect is obtained.

[0015] The present invention can be better understood by the detaileddescription and the accompanying drawings which will follow. It is notedthat these are to be considered simply illustrative of the invention,but are not to be considered restrictive to the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016]FIG. 1 is a sectional view of an optical fiber grating device asan embodiment of the present invention, which is a cross section of thegrating device cut by a plane including the optical axis.

[0017]FIG. 2 is a view showing a refractive index profile of the opticalfiber grating device of the embodiment.

[0018]FIG. 3 is a graph showing a transmission spectrum of the opticalfiber grating device.

[0019]FIG. 4 is a graph showing a relation between loss change Δα andthe thickness (c−b) of the second cladding region in the optical fibergrating device.

[0020]FIG. 5 is a graph showing a relation between the number oftransmission loss peaks and the relative refractive index difference Δn₂of the first cladding region in the optical fiber grating device.

[0021]FIG. 6 is a graph showing a relation between the number oftransmission loss peaks and the outside diameter 2 b of the firstcladding region in the optical fiber grating device.

[0022]FIG. 7 is a graph showing a relation between deviation Δλ oftransmission loss peak wavelength and exposure time to ultraviolet lightin formation of the grating in the optical fiber grating device.

BEST MODE FOR CARRYING OUT THE INVENTION

[0023] An embodiment of the present invention will be described below indetail with reference to the accompanying drawings. The same referencesymbols will denote the same or similar elements throughout thedescription of the drawings and redundant description will be omitted.

[0024]FIG. 1 is a sectional view of the optical fiber grating device 1as an embodiment of the present invention, which is a cross section ofthe grating device cut by a plane including the optical axis of anoptical fiber 10. FIG. 2 is a view showing a refractive index profile ofthe optical fiber grating device 1 of the present embodiment. Theoptical fiber grating device 1 of the present embodiment is a device inwhich a long period grating 14 is formed in the optical fiber 10 havinga core region 11, a first cladding region 12, and a second claddingregion 13 in the order named from the center of the optical axis and inwhich a resin coating 20 is provided around the optical fiber 10.

[0025] The core region 11 of the optical fiber 10 includes the center ofthe optical axis and has the refractive index n₁ and the outsidediameter 2 a, and the long period grating 14 is formed in apredetermined area of the core region 11. The first cladding region 12surrounds the core region 11 and has the refractive index n₂ and theoutside diameter 2 b. The second cladding region 13 surrounds the firstcladding region 12 and has the refractive index n₃ and the outsidediameter 2 c (normally, 125 μm). The resin coating 20 is provided aroundthe second cladding region 13 and has the refractive index n₄.

[0026] There are magnitude relations of n₁>n₂>n₃ and n₄>n₂ among therefractive indices of the core region 11, the first cladding region 12,the second cladding region 13, and the resin coating 20. The relativerefractive index difference Δn₂ of the first cladding region 12 to thesecond cladding region 13 is not less than 0.5% and preferably not morethan 1.5%. The relative refractive index difference Δn₂ (%) of the firstcladding region 12 to the second cladding region 13 is expressed by thefollowing equation:

Δn ₂=100×(n ₂ −n ₃)/n ₂  (1).

[0027] The relative refractive index difference Δn₁ (%) of the coreregion 11 to the first cladding region 12 is expressed by the followingequation:

Δn ₁=100×(n ₁ −n ₂)/n ₁  (2).

[0028] The thickness (c−b) of the second cladding region 13 is not lessthan λ and not more than 10λ, where λ is transmission loss peakwavelength. And more preferably, the thickness (c−b) is not less than1.5λ and not more than 10λ. Preferably, the outside diameter 2 b of thefirst cladding region 12 is not less than 100 μm and the mode fielddiameter of the fundamental mode propagating in the core region 11 isnot more than one tenth of the outside diameter 2 b of the firstcladding region 12.

[0029] When the relative refractive index difference Δn₂ of the firstcladding region 12 is not less than 0.5% as described above, the numberof transmission loss peaks is 4 or more in a predetermined wavelengthband (e.g., 1.2 μm to 1.8 μm) and the spacing is not more than 0.2 μmbetween the transmission loss peaks. When the thickness (c−b) of thesecond cladding region 13 with respect to the transmission loss peakwavelength λ is not less than λ, there is little influence from theouter layer outside the second cladding region 13 and the transmissionloss characteristics become stable. When the thickness (c−b) of thesecond cladding region 13 is not more than 10λ, the higher order modegenerated by the mode coupling at the transmission loss peak wavelengthis guided to the outside of the optical fiber 10 and the cutoff effectbecomes superior in the grating 14. When the device is designed asdescribed above, the coupling coefficient becomes small between the coremode and the higher order mode propagating in the first cladding regionand the variation is reduced in the transmission loss and transmissionloss peak wavelength against refractive index change. Accordingly,freedom of setting the grating period becomes large, controlling of thecutoff rate and transmission loss peak wavelength gets easy, andexcellent transmission loss characteristics is obtained in this opticalfiber grating device 1.

[0030] When the thickness (c−b) of the second cladding region 13 is notless than 1.5λ, the device reduces the wavelength dependence of thehigher order mode guided to the outside of the optical fiber 10, whichis preferable. When the refractive index n₄ of the resin coating 20provided around the second cladding region 13 is greater than therefractive index n₂ of the first cladding region 12, it becomes easierfor the higher order mode generated by the mode coupling at thetransmission loss peak wavelength, to go out to the outside of theoptical fiber 10, which is preferable. When the outside diameter 2 b ofthe first cladding region 12 is not less than 100 μm, the configurationis preferable in that the number of transmission loss peaks is large andis also preferable in that the cutoff effect is excellent. When the modefield diameter of the fundamental mode propagating in the core region 11is not more than one tenth of the outside diameter 2 b of the firstcladding region 12, the configuration is preferable in that the numberof transmission loss peaks is large and also in that the cutoff effectis excellent.

[0031] The optical fiber grating device 1 as described is produced, forexample, as follows. First prepared is the silica glass base opticalfiber 10 in which the core region 11 is doped with GeO₂ and the secondcladding region 13 with the fluorine (F) element. An ultraviolet laserbeam from a KrF excimer laser source is irradiated through anintensity-modulated mask of fixed period to the optical fiber 10 to formthe long period grating 14 therein. Then the resin coating 20 isprovided around the fiber 10.

[0032]FIG. 3 is a graph showing a transmission spectrum of the opticalfiber grating device 1. In this graph, a solid line (A) represents thetransmission spectrum of the optical fiber grating device 1 of theembodiment and a dashed line (B) a transmission spectrum of aconventional optical fiber grating device. The optical fiber 10 preparedherein was one wherein the core region 11 had the outside diameter 2 aof 3.5 μm, the first cladding region 12 had the outside diameter 2 b of105 μm, the second cladding region 13 had the outside diameter 2 c of125 μm, the relative refractive index difference Δn₁ of the core region11 to the first cladding region 12 was 1.1%, and the relative refractiveindex difference Δn₂ of the first cladding region 12 to the secondcladding region 13 was 0.7%. With the intensity-modulated mask havingthe pitch of 410 μm, the grating 14 was formed in the grating length of30 mm in the core region 11 of the optical fiber 10 to obtain theoptical fiber grating device 1. A light source was connected to one endof the optical fiber grating device 1 while a spectrum analyzer wasconnected to the other end of the optical fiber grating device 1. Inthis state the transmission spectrum of this optical fiber gratingdevice 1 was measured. As apparent from this graph, in the wavelengthband of 1.2 μm to 1.7 μm, the conventional optical fiber grating devicehas one transmission loss peak wavelength, whereas the optical fibergrating device 1 of the embodiment has five transmission loss peakwavelengths.

[0033]FIG. 4 is a graph showing a relation between the percentage ofloss change Δα and the thickness (c−b) of the second cladding region 13in the optical fiber grating device 1. The horizontal axis of this graphis of the logarithmic scale. The percentage of loss change Δα (%) isexpressed by the following equation:

Δα=100×(α₂−α₁)/α₂  (3),

[0034] where the loss α₁ is a value measured at the loss peak wavelengthin the 1.55 μm wavelength band in the configuration without the resincoating 20 around the optical fiber 10 and thus with air (refractiveindex 1.0) instead around the optical fiber 10 and the loss α₂ is avalue measured at the loss peak wavelength in the 1.55 μm wavelengthband in the configuration with matching oil (having the refractive indexof 1.45 approximately equal to that of silica glass) around the opticalfiber 10. The percentage of loss change Δα is preferably as small aspossible, in order to decrease the change of loss. The outside diameter2 a of the core region 11 was 3.5 μm, the outside diameter 2 c of thesecond cladding region 13: 125 μm, the relative refractive indexdifference Δn₁ of the core region 11: 1.1%, and the relative refractiveindex difference Δn₂ of the first cladding region 12: 0.7%. The outsidediameter 2 b of the first cladding region 12 was either of the values inthe graph.

[0035] As apparent from this graph, the percentage of loss change Δαsuddenly decreases as the thickness (c−b) of the second cladding region13 exceeds 1 μm. When this is expressed with respect to the transmissionloss peak wavelength λ, the thickness (c−b) of the second claddingregion 13 is preferably not less than λ, because the percentage of losschange Δα is small in the specified range. The grating 14 formed in thecore region 11 of the optical fiber grating device 1 needs to be a longperiod grating that can expel the higher order mode generated by themode coupling at the transmission loss peak wavelength, to the outsideof the optical fiber. However, if the thickness (c−b) of the secondcladding region 13 is too large, the higher order mode will propagate inthe second cladding region 13 to weaken cutoff effect at the grating 14.Therefore, the thickness (c−b) of the second cladding region 13 ispreferably not more than 10λ.

[0036]FIG. 5 is a graph showing a relation between the number oftransmission loss peaks and the relative refractive index difference Δn₂of the first cladding region 12 in the optical fiber grating device 1.The optical fibers 10 prepared herein were those having the outsidediameter 2 a of the core region 11: 3.5 μm, the outside diameter 2 b ofthe first cladding region 12: 105 μm, the outside diameter 2 c of thesecond cladding region 13: 125 μm, and the relative refractive indexdifference Δn₁ of the core region 11: 1.1%. The fluorine was added ineither of various doping amounts in the first cladding region 12 toproduce the optical fibers with respective values of the relativerefractive index difference Δn₂ of the first cladding region 12. Thenumber of transmission loss peaks represents the number of transmissionloss peaks in the wavelength band of 1.2 μm to 1.8 μm. As apparent fromthis graph, the number of transmission loss peaks becomes larger as therelative refractive index difference Δn₂ of the first cladding region 12increases. When the relative refractive index difference Δn₂ of thefirst cladding region 12 is not less than 0.5%, the number oftransmission loss peaks is 4 or higher in the wavelength band of 1.2 μmto 1.8 μm and the spacing between the transmission loss peaks is notmore than 0.2 μm, which is preferable.

[0037]FIG. 6 is a graph showing a relation between the number oftransmission loss peaks and the outside diameter 2 b of the firstcladding region 12 in the optical fiber grating device 1. The opticalfibers 10 prepared herein were those having the outside diameter 2 a ofthe core region 11: 3.5 μm, the outside diameter 2 c of the secondcladding region 13: 125 μm, the relative refractive index difference Δn₁of the core region 11: 1.1%, and the relative refractive indexdifference Δn₂ of the first cladding region 12: 0.7%. The optical fiberswere produced with respective values of the outside diameter 2 b of thefirst cladding region 12. The number of transmission loss peaksrepresents the number of transmission loss peaks in the wavelength bandof 1.2 μm to 1.8 μm. As apparent from this graph, the number oftransmission loss peaks increases as the outside diameter 2 b of thefirst cladding region 12 increases. When the outside diameter 2 b of thefirst cladding region 12 is not less than 60 μm, the number oftransmission loss peaks is 3 or higher; when the outside diameter 2 b ofthe first cladding region 12 is not less than 72 μm, the number oftransmission loss peaks is 4 or higher; when the outside diameter 2 b ofthe first cladding region 12 is not less than 100 μm, the number oftransmission loss peaks is 6 or higher. Since the thickness (c−b) of thesecond cladding region 13 needs to be not more than 10λ as describedpreviously, it is preferable that the outside diameter 2 b of the firstcladding region 12 be not less than 100 μm when the outside diameter 2 cof the second cladding region 13 is 125 μm.

[0038]FIG. 7 is a graph showing a relation between deviation Δλ of thetransmission loss peak wavelength and the exposure time to theultraviolet light in the formation of the grating 14 in the opticalfiber grating device 1. This figure also shows Comparative Example 1(indicated by L2) and Comparative Example 2 (indicated by L3) inaddition to Example (indicated by L1). The optical fibers 10 prepared inExample were those having the outside diameter 2 a of the core region11: 3.5 μm, the outside diameter 2 b of the first cladding region 12:105 μm, the outside diameter 2 c of the second cladding region 13: 125μm, the relative refractive index difference Δn₁ of the core region 11:1.1%, and the relative refractive index difference Δn₂ of the firstcladding region 12: 0.7%. The optical fibers prepared in ComparativeExample 1 were those having the refractive index profile shown in FIG.2, but having the outside diameter 2 a of the core region 11: 3.5 μm,the outside diameter 2 b of the first cladding region 12: 40 μm, theoutside diameter 2 c of the second cladding region 13: 125 μm, therelative refractive index difference Δn₁ of the core region 11: 1.1%,and the relative refractive index difference Δn₂ of the first claddingregion 12: 0.3%. The optical fibers prepared in Comparative Example 2were those having a simple refractive index profile consisting of a coreregion and a cladding region, in which the outside diameter of the coreregion was 3.5 μm, the outside diameter of the cladding region 125 μm,and the relative refractive index difference of the core region 1.1%. Inall of Example, Comparative Example 1, and Comparative Example 2, thepitch of the intensity-modulated mask was 410 μm and the irradiationpower of ultraviolet light was identical.

[0039] As apparent from this graph, in all of Example, ComparativeExample 1, and Comparative Example 2, the transmission loss peakwavelength deviates to the longer wavelength side with increase in theexposure time to the ultraviolet light, so as to increase the deviationΔλ of the transmission loss peak wavelength. The increase of thedeviation Δλ of the transmission loss peak wavelength against theexposure time to ultraviolet light in Example is smaller than that inthe case of Comparative Example 1 and approximately equal to that in thecase of Comparative Example 2. Accordingly, the present embodimentensures a wide range of exposure time to ultraviolet light to achievethe desired transmission loss peak wavelength and transmission loss inthe formation of the grating 14, thus facilitating attainment of thedesired transmission loss peak wavelength and transmission loss.

INDUSTRIAL APPLICABILITY

[0040] In the optical fiber grating device of the present invention, thenumber of transmission loss peaks is large in the predeterminedwavelength band (e.g., 1.2 μm to 1.8 μm) and the spacing is smallbetween the transmission loss peaks. The coupling coefficient is alsosmall between the core mode and the higher order mode propagating in thefirst cladding region, so that variation is reduced in the transmissionloss and transmission loss peak wavelength against refractive indexchange. Further, there is little influence from the outer layer outsidethe second cladding region and the transmission loss characteristics arestable, so as to achieve the excellent cutoff effect in the grating.Accordingly, the optical fiber grating device provides high degrees offreedom in the setting of the grating period and permits easy control ofthe transmission loss and transmission loss peak wavelength, so as to besuperior in the transmission loss characteristics.

[0041] It is obvious that the present invention can be modified orchanged in various ways, from the above description of the presentinvention. Such modifications and changes are to be considered not todepart from the essence and scope of the present invention, and allimprovements obvious to those skilled in the art are to be considered tofall within the scope of the claims which follow.

1. An optical fiber grating device in which a long period grating isformed in a core region of an optical fiber comprising the core regionhaving a refractive index n₁ and an outside diameter 2 a, a firstcladding region surrounding the core region and having a refractiveindex n₂ and an outside diameter 2 b, and a second cladding regionsurrounding the first cladding region and having a refractive index n₃and an outside diameter 2 c, wherein there is a magnitude relation ofn₁>n₂>n₃ among the refractive index n₁ of the core region, therefractive index n₂ of the first cladding region, and the refractiveindex n₃ of the second cladding region, wherein a relative refractiveindex difference of the first cladding region to the second claddingregion is not less than 0.5%, and wherein a thickness (c−b) of thesecond cladding region with respect to a transmission loss peakwavelength λ is in a range of not less than λ nor more than 10λ.
 2. Theoptical fiber grating device according to claim 1, wherein the relativerefractive index difference of the first cladding region to the secondcladding region is not less than 0.5% nor more than 1.5%.
 3. The opticalfiber grating device according to claim 1, wherein a resin coatinghaving a refractive index n₄ (where n₄>n₂) is provided around saidsecond cladding region.
 4. The optical fiber grating device according toclaim 1, wherein the outside diameter 2 b of the first cladding regionis not less than 100 μm.
 5. The optical fiber grating device accordingto claim 1, wherein a mode field diameter of fundamental modepropagating in the core region is not more than one tenth of the outsidediameter 2 b of the first cladding region.